Question
The speed of a car is 60% more than the speed of a bus.
The train can cover (d-250) km distance in (t-3.5) hours. The car covers (d+140) km distance in (t-2) hours. The speed of train is 2.4 times the difference between the speed of bus and car. The distance travelled by bus is 1500 km in which it will take (t+4) hours, then which of the following statements is/are true? (i) The value of ‘t’ is an odd number. (ii) The value of ‘d’ is a three digit number. (iii) The ratio between the distance travelled by bus and train is (6t+2) : (3t+3) respectively.Solution
Let’s assume the speed of car is ‘8a’. The speed of a car is 60% more than the speed of a bus. 8a = (100+60)% of speed of a bus 160% of speed of a bus = 8a 1.6 x speed of a bus = 8a speed of a bus = 5a The speed of train is 2.4 times the difference between the speed of bus and car. speed of train = 2.4x(8a-5a) = 2.4x3a = 7.2a The train can cover (d-250) km distance in (t-3.5) hours. 7.2a = (d-250)/(t-3.5) a = (d-250)/7.2(t-3.5)  Eq.(1) The car covers (d+140) km distance in (t-2) hours. 8a = (d+140)/(t-2) a = (d+140)/8(t-2)  Eq.(2) The distance travelled by bus is 1500 km in which it will take (t+4) hours. 5a = 1500/(t+4) a = 300/(t+4)  Eq.(3) So Eq.(1) = Eq.(2) (d-250)/7.2(t-3.5) = (d+140)/8(t-2) (d-250)/0.9(t-3.5) = (d+140)/(t-2) (d-250)/(0.9t-3.15) = (d+140)/(t-2) d = (376t−941)/(0.1t+1.15)  Eq.(4) So Eq.(1) = Eq.(3) (d-250)/7.2(t-3.5) = 300/(t+4) (d-250)/(t-3.5) = 2160/(t+4) d = (2410t−6560)/(t+4)  Eq.(5) So Eq.(4) = Eq.(5) (376t−941)/(0.1t+1.15) = (2410t−6560)/(t+4) After solving the above equation, t = 8, 3.5 But if t = 3.5, then the time taken by train to cover distance will be zero which is not possible. So t = 8 . Put the value of ‘t’ in Eq.(4). d = (376x8−941)/(0.1x8+1.15) = (3008−941)/(0.8+1.15) = 2067/1.95 = 1060 (i) The value of ‘t’ is an odd number. The above given statement is not true. Because the value of ‘t’ cannot be an odd number. (ii) The value of ‘d’ is a three digit number. The above given statement is not true. Because the value of ‘d’ is not a three digit number. (iii) The ratio between the distance travelled by bus and train is (6t+2) : (3t+3) respectively. distance travelled by bus and train = (6t+2) : (3t+3) = 5ax(t+4) : 7.2ax(t-3.5) Put the value of ‘t’ in the above equation. (6x8+2) : (3x8+3) = 5x(8+4) : 7.2x(8-3.5) (48+2) : (24+3) = 5x12 : 7.2x4.5 50 : 27 = 50 : 27 The above given statement is true. Because the above given expression is satisfied.
Walking 3/4 of his normal speed, Ravi was 21 minutes late in reaching his office. The usual time took to cover the distance between his home and office ...
A train moves at 90 km/h and needs to cover a journey in 2 hours. It halts for 10 minutes at the midpoint. What speed must it take for the second half?
A thief stole Mayank’s purse and the theft is reported at 10 am and police started chasing the thief at 1:00pm. How much time the police took to c...
Ravi decides to increase his cycling speed from 18 km/h to 24 km/h and ends up travelling 54 km more in the same amount of time. How far did he go at th...
- The ratio of the speeds of Priya and Diya is 6:5 respectively. Sneha can cover 720 km in 12 hours. If the speed of Diya is 20% less than that of Sneha, how...
A cyclist covers 120 km in 6 hours. The speed of a motorbike is 10 km/h more than the speed of the cyclist. Find the time taken by the motorbike (in min...
Aman takes 2 hours to bike from point 'M' to point 'N' at a speed of 25 km/h. He then increases his speed by 80% and takes 3 hours to reach point 'O' fr...
A train overtakes two persons walking along a railway track. The first one walks at 3.2 Km/h. The other one walks at 4.5 Km/h. The train needs 5.5 and 5...
A train is travelling at the rate of 45 km/hr. How many seconds it will take to cover a distance of 5/8 km?
Robert started his journey on Monday and travelled at constant speed. Next day by 10.30 am, he had covered 4/7 of his whole journey and on the same day ...